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-Dominant- [34]
3 years ago
15

Hazel has an assortment of red, blue, and green balls. The number of red balls is 2/3 the number of blue balls. The number of gr

een balls is 1 more than 1/3 the number of blue balls. In total, she has 15 balls.
An equation created to find the number of blue balls will have

- no solution
- one solution
- infinitely many solutions
Mathematics
2 answers:
Lubov Fominskaja [6]3 years ago
8 0

Answer:

x = 4\frac{2}{3}      y = 7        and    z =3\frac{1}{3}

This implies the equation has just one solution

Step-by-step explanation:

To create the equation, we need to be able to write the information  or interpret the question mathematically.

Let x equal to the number of red balls.

Let y equal to the number of blue balls.

Let z equal to the number of green balls.

From the question; "The number of red balls is 2/3 the number of blue balls" can be mathematically written as :  x = \frac{2}{3} y  ---------------------------(1)

The next statement; "The number of green balls is 1 more than 1/3 the number of blue balls" can be written mathematically as: z = 1+\frac{1}{3} y ----------------------------(2)

The next statement; "she has 15 balls."  can be mathematically written as:     x + y + z = 15 ----------------------------------------(3)

Substitute  equation (1) and equation (2) into equation (3)

\frac{2}{3} y + y +1 +\frac{1}{3} y  =  15

We can rearrange this equation

\frac{2}{3} y  +\frac{1}{3} y + y +1 =  15

\frac{3}{3} y  + y + 1 = 15

y + y + 1 = 15

2y + 1 = 15

subtract 1 from both-side of the equation

2y + 1 -1 = 15 -1

2y = 14

Divide both-side of the equation by 2

2y/2 = 14/2

y = 7

Substitute y = 7 into equation (1)

x = \frac{2}{3} y

x = \frac{2}{3} (7)

x = 14/3

x = 4\frac{2}{3}

Substitute y= 7 in equation (2)

z = 1+\frac{1}{3} y

z = 1+\frac{1}{3} (7)

z = 1+ 7/3

z = 10/3

z =3\frac{1}{3}

Therefore;

x = 4\frac{2}{3}      y = 7        and    z =3\frac{1}{3}

This implies the equation has just one solution.

Korvikt [17]3 years ago
3 0
It would have one solution since you know the total number of balls
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Find the volume of a pyramid with a square base, where the side length of the base is
ValentinkaMS [17]

Answer:

<h2>1529.4 m³</h2>

Step-by-step explanation:

Volume of a pyramid can be found by using the formula

v =  \frac{1}{3}  \times a \times h \\

a is the area of the base

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Since the base is a square we have

v =  \frac{1}{3}  \times  {15.3}^{2}  \times 19.6 \\  = 78.03 \times 19.6 \\  = 1529.388

We have the final answer as

<h3>1529.4 m³</h3>

Hope this helps you

3 0
3 years ago
HELP!!!!!
Elis [28]

Line 1 and line 4 are parallel

Step-by-step explanation:

Two lines are said to be parallel if they have same slope.

In order to compare the lines given, we have to write them all in the same form, and then compare their slopes.

Line 1:

y=\frac{1}{3}(x+6)

Applying distributive property,

y=\frac{1}{3}x+2

Line 2:

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y=-3(x-4)

Applying  distributive property,

y=-3x+12

Line 4:

3y+18=x

re-arranging,

3y=x-18\\y=\frac{1}{3}x-6

Now we have rewritten all the lines in the form y=mx+q, where m is the slope. By comparing the values of m, we see:

m_1 = \frac{1}{3}\\m_2=3\\m_3 = -3\\m_4=\frac{1}{3}

Therefore, the lines which are parallel are line 1 and line 4.

Learn more about parallel and perpendicular lines:

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3 years ago
The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
kap26 [50]

Answer:

If r >> h, the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

A = \pi \cdot r^{2} + 2\pi\cdot s

Where:

r - Base radius of the cone, measured in inches.

s - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

s = \sqrt{r^{2}+h^{2}}

Where h is the altitude of the cone, measured in inches. If r >> h, then:

s \approx r

And:

A = \pi\cdot r^{2} +2\pi\cdot r

Given that A = 1885.7143\,in^{2}, the following second-order polynomial is obtained:

\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2}  = 0

Roots can be found by the Quadratic Formula:

r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}

r_{1,2} \approx -1\,in \pm 24.521\,in

r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

3 0
3 years ago
Find the cross product of <img src="https://tex.z-dn.net/?f=-%20%5Cfrac%7B3%7D%7B4%7Dv" id="TexFormula1" title="- \frac{3}{4}v"
dsp73
For any scalars c_1,c_2, we have

c_1\mathbf v\times c_2\mathbf w=c_1c_2\mathbf v\times\mathbf w

So

\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\mathbf v\times\mathbf w

We have

\mathbf v\times\mathbf w=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\-2&12&-3\\-7&4&-6\end{vmatrix}
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which makes

\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\begin{bmatrix}-60\\9\\76\end{bmatrix}=\begin{bmatrix}-\frac{45}2\\\\\frac{27}8\\\\\frac{57}2\end{bmatrix}
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3 years ago
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arlik [135]

Answer:

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5 0
3 years ago
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